Let P n be a collection of n points on the plane. For a pair of points u and v P n let C(u,v) be the minimum number of points of P n contained in any circle contaning u and v. In this paper we prove the result that there exist two points u o and v o P n such that any circle containing u o and v o contains at least È(n-2)/60˘ elements of P n (other than u o and v o). We also prove that the avera...

Let G(V,E) be a graph with p vertices and q edges. A graph G is said to have an odd mean labeling if there exists a function f : V (G) → {0, 1, 2,...,2q - 1} satisfying f is 1 - 1 and the induced map f* : E(G) → {1, 3, 5,...,2q - 1} defined by f*(uv) = (f(u) + f(v))/2 if f(u) + f(v) is evenf*(uv) = (f(u) + f(v) + 1)/2 if f(u) + f(v) is odd is a bijection. A graph that admits an odd mean labelin...

This study reports the fabrication of n-TiO2/p-Si hetrojunction by deposition of TiO2nanowires on p-Si substrate. The effect of system pressure and the current-voltage (I-V) characteristics of n-TiO2/p-si hetrojunction were studied. The morphology of the samples was investigated by Field Emission Scanning Electron Microscopy (FESEM) which confirms formation of T...

background: development of an effective vaccine is highly needed in order to restrict the aids pandemic. dna vaccines initiate both arms of immunity without the potential of causing disease. hiv-1 p24 and gp41 (gag and env) proteins play important roles in viral pathogenesis and are effective candidates for immune induction and vaccine design. objective: in this study, new dna vaccine candidate...

Sonlu bir Z_n grubunun yönlendirilmemiş P(Z_n ) power grafı, köşelerinin kümesi olan bağlantılı graftır ve burada iki köşe komşudur gerek yeter şart u≠v ⊆ veya dir. 〖(Z〗_n,+) grubuna karşılık gelen Yönlendirilmemiş G=P(Z_n grafının Hyper-Wiener, SK, 〖SK〗_1, 〖SK〗_2 Harary indeksleri sırasıyla, 1/2 ∑_({u,v}⊆V(G))▒〖d(u,v)〗+1/2 ∑_({u,v}⊆V(G))▒〖d^2 (u,v) 〗 ∑_(uv∈E(G))▒〖d(u)+d(v)〗, ∑_(uv∈E(G))▒〖d(u)....

objective: epilepsy is a chronic neurological disorder requiring long term therapy using antiepileptic medications. reports have incriminated long term antiepileptic drugs use in deficiency of vitamin d and bone diseases in all age groups. to investigate the association between serum 25-hydroxyvitamin d levels and pediatric epilepsy in indian patients.           methods& methods: we prospective...

A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...

Given a connected graph G = ( V , E ) $G=(V,E)$ and length function ℓ : → R $\ell :E\to {\mathbb{R}}$ we let d v w ${d}_{v,w}$ denote the shortest distance between vertex $v$ $w$ . A t $t$ -spanner is subset ′ ⊆ $E^{\prime} \subseteq E$ such that if ${d}_{v,w}^{^{\prime} }$ denotes distances in subgraph $G^{\prime} =(V,E^{\prime} )$ then ≤ }\le t{d}_{v,w}$ for all ∈ $v,w\in V$ We study size of ...

We consider the following Keller-Segel system with gradient dependent chemotactic coefficient: \begin{document}$ \begin{equation*} \begin{cases} u_{t} = \Delta u- \chi \nabla\cdot (uf(|\nabla v|)\nabla v),\\ 0 v -v+g(u), \end{cases} \end{equation*} $\end{document} in smooth bounded domains $ \Omega \subset \mathbb{R}^{n}, \,n\geq 1 f(\xi) \big(\xi^{p-2}\big(1+\xi^{p}\big)^{\frac{q-p}{p}}\big), ...

Given a minimal model of an elliptic curve, $E/K$, over finite extension, $K$, ${\mathbb Q}_{p}$ for any rational prime, $p$, and point $P \in E(K)$ infinite order, we determine precisely $\min \left( v \phi_{n}(P) \right), \psi_{n}^{2}(P) \right) \right)$, where $v$ is normalised valuation on $K$ $\phi_{n}(P)$ $\psi_{n}(P)$ are polynomials arising from multiplication by $n$ this the curve.